Mathematics

This talk gives an overview of stochastic modeling and analysis of a large 3-dimensional array of geospatial porosity data. The analysis is based on empirical methods for covariance estimation on horizontal cross sections of the data using singular value decomposition (SVD) for principal component analysis (PCA) together with a kernel (KPCA) method yielding dimension reduction. The results can be used to produce simulated data with characteristics mimicking those of the original porosity observations. In particular simulated realizations conditioned on a small subarray of the the original observations effectively reproduce observed channeling, an important large scale feature of interest in the sub-surface relevant to transport of contaminates. This is joint work with Malgo Peszynska (OSU Mathematics) and Lisa Madsen (OSU Statistics).